I thought that too. The prompt is full of metaheuristics.

I remember a couple of years back when people were saying how prompt engineering was a skill, and reading this prompt kinda took me back to that.

Were I to guess, the reason the model couldn't do this itself is because most of the time, for most problems, a lot of this is bad advice.

In search optimisation you're often trading between time and quality. A very broad search will return very bad results for a long time. Where as a more depth oriented search with some heuristic will tend to return a pretty good result (if not optimal or close to optimal) quickly.

I'd assume models naturally want to find some middle ground there because that's the best thing to do most of the time, but for very difficult problems where a decent attempt isn't good enough you want a much broader search that doesn't have the time constraints. Much of the prompt seemed to be in that direction – really encouraging broadness of the search, preventing early convergence, and remove pressure of time constraints.